1 Introduction

The activation analysis was made in 1934 by Irene Joliot Curie and Frederic Joliot who used alpha particles for bombarded aluminum, boron and magnesium [1,2,3]. In 1936, the activation analysis was done for element analysis by Hevesy and Levi who bombarded dysprosium and europium by neutrons [1, 3]. Two years later, in 1938, Seaborg and Livingood bombarded the iron sample with deuterons for the determination of the gallium [3]. Therefore, it can be concluded that the selection of the source for activation analysis is important. One of the practical sources for activation analysis is neutron. For this aim, several neutron sources exist today, including nuclear reactors, accelerators, and isotopic sources. As mentioned above, the neutron activation analysis was introduced for element analysis many years ago since it is a nondestructive analysis. Therefore, in this work, we used thermal neutrons for activation of samples. In this method, the nucleus of the target is bombarded by thermal neutrons. When a thermal neutron capture by a nucleus is done, one or more prompt characteristic gamma released rapidly of the compound nucleus [4,5,6] and this is called as the thermal neutron activation analysis (TNAA). We could detect these prompt gammas by suitable gamma detectors (such as solid-state detectors [7,8,9] and scintillator detectors [10,11,12]) and this is also called as prompt gamma neutron activation analysis (PGNAA). One can find good literature for recent developments and applications of PGNAA in Ref. [13]. However, the sensitivity of PGNAA depends on the thermal neutron flux. Therefore, the nuclear reactors are more commonly used because of their high considerable neutron flux. But nuclear reactors are expensive and cannot be used everywhere. Therefore, we need another neutron source that has acceptable neutron flux and is cheaper and portable. One of the neutron sources having previous conditions is the neutron source that has been generated by an electron linear accelerator (LINAC) [14]. Recently, many works have been done on the development of neutron sources generated by electron LINAC [15,16,17,18]. These sources could be used to detect explosives based on the thermal neutron activation, for example, one can find the other works [19, 20]. However, in this study, we used a 10 MeV electron LINAC for investigation of feasibility of explosives detection (TNT, PETN, RDX, HMX, NG and EGDN) based on TNAA. For this aim, we optimized an e–γ–n converter to reach suitable high thermal neutron flux using MCNPX 2.7 Monte Carlo code [21]. It should be mentioned that there are other portable neutron sources also, which have been used to detect explosives such as neutron generators (D–D and D–T) [22,23,24], californium-252 [24,25,26,27] and americium–beryllium [24, 28, 29]. However, for optimization of the e–γ–n converter, we studied ten suitable materials to use as neutron collimator/reflector. Finally, the BeD2 was chosen as the best material. Also, the optimized length of the collimator was chosen as 60 cm by Monte Carlo simulation. Because of an intense bremsstrahlung photons flux that emitted from the aperture of the e–γ–n converter along with neutrons we chose 30 cm Lead by Monte Carlo simulation to reduce intense photons flux. After all of simulation and optimization of e–γ–n converter, we could reach to 4.78 × 108 ± 0.63% (n/cm2 mA s) total neutron flux and 3.95 × 108 ± 0.69% (n/cm2 mA s) thermal neutron flux. The neutron flux can collide with explosives and activate the elements of them (H, C, N, O) through neutron capture reaction. Therefore, we need a suitable gamma detector to record the prompt gamma rays. For this aim, twelve LaBr3 (3-inch) were simulated, because the LaBr3 detector has a better resolution than the NaI detector and also has greater density and faster decay time [30]. The LaBr3 also is cheaper than HPGe detector and there is no need to use liquid nitrogen for cooling [30]. Note that liquid nitrogen of the HPGe detector can trouble the spectrum of prompt gamma rays of nitrogen emitted from explosives. After collecting the prompt gamma rays spectrum, we observed the peaks of prompt gamma of H and N clearly (at 2.223 MeV and 10.829 MeV, respectively). Finally, we could calculate the ratio of the counts under the peaks of H and N along with a good agreement between the results of simulation and theory. This agreement showed that we can use a 10 MeV LINAC for TNAA and explosive detection, as well. In addition, note that the dependency of converter dimensions on linear accelerator dimensions is important, because different accelerators have different dimensions. Certainly, in the future studies, the converter designed in this paper should be considered in terms of photon and neutron dosimetry. Since neutrons and photons can escape this converter and as a final point, it should be noted that the converter designed in this work can also be used in boron neutron capture therapy [31], nuclear waste transmutation [32], and isotope production [33].

2 Materials and method

In the present paper, the MCNPX 2.7 Monte Carlo code has been used for all simulations. The MCNPX is a comprehensive 3-dimentional Monte Carlo code that it can simulate many particles (such as electron, photon and neutron, etc.) and reactions (such as atomic and nuclear reaction) [21]. For simulation of the electron, photon and neutron el03, mcplib04 and ENDF/B-VII.0 cross section library have been used, respectively (el03, mcplib04, and ENDF/B-VII.0 are the name of the cross section library of the electron, photon, and neutron in the MCNP code, respectively). However, we used a 10 MeV LINAC as an electron source with the properties mentioned in Ref. [34] (the accelerating tube length of a 10 MeV electron LINAC can be 1.6 m [35] or 1.7 m [36]) and in order to define the electron source card in the MCNPX, we used from Ref. [14]. Also, LaBr3 (3-inch) scintillator detector has been used to obtain the prompt gamma spectrum emitted from the explosives [37].

3 The e–γ–n converter optimization

In this work, we used a 10 MeV LINAC for generation of a good neutron source. For this aim, we used a good reference that designed an e–γ–n converter based on 10 MeV LINAC [34]. But in our work, in order to use in TNAA, we studied again the previous design for suitable optimization. Note that we only studied the length and the material type of the collimator of the previous e–γ–n converter and did not change the other parts of the e–γ–n converter. After all optimizations and changes mentioned (in detail) in the following, the new optimized cylindrical e–γ–n converter based on the 10 MeV electron LINAC is shown in Fig. 1. Briefly, the method of generation of a neutron source from an electron accelerator is that the energetic electrons collide with a high atomic number target (such as tungsten) and lead to a relatively intense flux of bremsstrahlung photons and then these photons collide with a photonuclear target (such as beryllium or heavy water) and lead to a significant neutrons flux. For more information on the e–γ–n converter design method, one can see Ref. [14].

Fig. 1
figure 1

Scheme of optimized the cylindrical e–γ–n converter based on 10 MeV electron LINAC, part A from Ref. [34] and part B from the present work (the 2D view) (all dimensions are in cm)

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Ten materials (Be, BeD2, BeO, D2O, graphite, Al2O3, H2O, PE, ZrH2, and Pb) have been studied for the determination of the best collimator and reflector by MCNPX 2.7 Monte Carlo Code (along with ENDF/B-VII.0 neutron cross section library) whose properties are shown in Table 1. Also, the length of the collimator (the distance between the aperture and D2O target as a gamma-neutron converter) has been investigated. Four parameters have been studied for determination of the best material. These parameters include \( C_{1} = \emptyset_{\text{th}}^{2} /\emptyset_{\text{total}} \left( {{\text{n}}/{\text{cm}}^{2} \;{\text{mA}}\;{\text{s}}} \right) \), \( {\text{C}}_{2} = \emptyset_{\text{th}} /\emptyset_{\text{epi}} \), \( {\text{C}}_{3} = \emptyset_{\text{th}} /\emptyset_{\text{fast}} \) and \( {\text{C}}_{4} = \emptyset_{\text{th}} /\emptyset_{{\left( {{\text{epi}} + {\text{fast}}} \right)}} \) where \( \emptyset_{\text{th}} ,\;\emptyset_{\text{epi}} ,\;\emptyset_{\text{fast}} \) and \( \emptyset_{\text{total}} \) are thermal (< 10−6 MeV), epithermal (10−6–10−2 MeV), fast (> 10−2 up to 20 MeV) and total neutron flux, respectively [38] (Fig. 2). The parameter C1 is called the thermalization efficiency. This parameter can be used to select the point which has maximize the ratio of the thermal neutron flux to the total neutron flux and has the highest possible value of the thermal neutron flux [38].

Table 1 The properties of materials utilized in the e–γ–n converter optimization [16, 38, 39]
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Fig. 2
figure 2

The parameter a C1, b C2, c C3 and d C4 as a function of distance between D2O and aperture

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For more confidence in the optimization of the distance between D2O to aperture, the thermal neutron flux has been investigated, as shown in Fig. 3. It should be noted that the aperture diameter is considered 40 cm, because we intend to optimize the e–γ–n converter based on practical cases. One of the practical cases is detecting possible explosives in the luggage of airport passengers by TNAA. Note that the common approved size of the luggage based on some popular airlines such as United Airlines, American Airlines and Lufthansa Airlines is (56 cm × 35 cm × 22 cm) [40], (56 cm × 36 cm × 23 cm) [41] and (55 cm × 40 cm × 23 cm) [42], respectively (in format: length × width × height). Given that the increase in thermal neutron flux is desirable in this work, see Figs. 2 and 3, the BeD2 has been chosen as the best material (because for example, the BeD2 relative to Be and graphite can increase the thermal neutron flux up to 14% and 113%, respectively, that these percentages are based on the relative difference relationship) for use as a collimator/reflector and also the optimized length of the collimator (distance between D2O and aperture) has been chosen as 60 cm.

Fig. 3
figure 3

Thermal neutron flux as a function of distance between D2O and aperture

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As mentioned above, an intense bremsstrahlung photon flux along with the neutron flux is emitted from the aperture of the converter. We tried to reduce the intensity of these photons as much as possible, because these bremsstrahlung photons can be recorded in the spectrum of the gamma detector acting as a background signal overlapping to the prompt gamma spectrum emitted from the explosive elements. Therefore, we used lead to reduce the bremsstrahlung photon flux. In fact, we placed the lead right after heavy water and to find the optimum thickness of lead, we used the Monte Carlo simulation for which the results are shown in Fig. 4. See Fig. 4, the optimum thickness of lead is 30 cm. Note that lead leads to a decrease in thermal neutron flux, as well, that it is not significant as shown in Fig. 4. But the thickness of the 30 cm lead is capable of reducing the photon flux (in the energy range of 0.5-10 MeV) by approximately 105 times which is very significant (Table 1).

Fig. 4
figure 4

Photon flux (in the energy range of 0.5–10 MeV) and thermal neutron flux as a function of the thickness of lead

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The emitted neutron spectrum from the optimized e–γ–n converter is shown in Fig. 5 that the total neutron flux and thermal neutron flux are 4.78 × 108 ± 0.63% (n/cm2 mA s), 3.95 × 108 ± 0.69% (n/cm2 mA s), respectively. Now, we can use these neutrons as a desirable neutron source for explosive detection based on TNAA. The angular distribution of neutron and photon beams emitted from the aperture of the converter is shown in Figs. 6 and 7 (as a contour plot), respectively.

Fig. 5
figure 5

Neutron energy spectrum according to the optimized e–γ–n converter (Fig. 1)

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Fig. 6
figure 6

Neutron tracks (per electron) have been shown for the right side of the aperture in Fig. 1 and note that the origin of the horizontal axis (X-axis) has been placed on the tungsten target

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Fig. 7
figure 7

Photon tracks (per electron) have been shown for the right side of the aperture in Fig. 1 and note that the origin of the horizontal axis (X-axis) has been placed on the tungsten target

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4 Results and discussion

4.1 Simulation of TNAA

As shown in the previous section, we obtained a suitable neutron spectrum with acceptable flux for use in explosives detection based on TNAA. To perform the Monte Carlo simulation, we chose six commonly cylindrical sample explosives (TNT, PETN, RDX, HMX, NG, and EGDN) with a mass of 1 kg and a radius of 5 cm for which the properties are listed in Table 2. The commonly explosives are made up of four elements: hydrogen, nitrogen, carbon, and oxygen (Table 2). After the thermal neutron capture reaction, hydrogen, nitrogen, carbon, and oxygen elements emitted one, eighteen, four, and three prompt gamma rays, respectively [43] and we observed all of prompt gamma rays of H, N, C, and O by F1 tally (current integrated over a surface [21]) using ENDF/B-VII.0 neutron cross section library.

Table 2 The properties of six commonly explosives [39]
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But, in this study, the F1 tally is not desired, because we are looking for the response function of the gamma ray detector to analyze the spectrum of the prompt gamma rays emitted by the explosives, and therefore, we used F8 tally (energy distribution of pulses created in a detector by radiation [21]). In this work, we used twelve LaBr3 (3-inch), because no variance reduction cards can be used to reduce statistical errors when using the F8 tally along with neutron source in MCNPX code [21]. Therefore, we tried to reduce the statistical error by increasing the number of detectors. The setup of twelve LaBr3 gamma detectors is shown in Fig. 8. Note that the distance of detectors from the center of the cylindrical explosives is 21 cm, because the radius of aperture of the e–γ–n converter is 20 cm. The LaBr3 detector is an interesting gamma-ray detector for TNAA because of its faster decay time, higher density and better resolution than the NaI detector and also it is cheaper than the HPGe detector and there is no need to use liquid nitrogen for cooling [30]. For the simulation of the gamma detectors, we used the F8 tally along with FT (special treatments for tallies [21]) and GEB (Gaussian energy broadening [21]) cards in order to apply full-width of half maximum (FWHM) on all of the LaBr3 detectors. The MCNPX code uses the following equation as the FWHM (in MeV) function [21].

$$ {\text{FWHM}} = A + B\sqrt {E + CE^{2} } $$
(1)

where E is energy of photon in MeV, A, B and C are coefficients in MeV, (MeV)1/2, and (MeV)−1, respectively. We found the coefficients A, B and C through fitting data of Ref. [37] as − 0.007836, 0.03858 and 0.001, respectively.

Fig. 8
figure 8

Setup of twelve LaBr3 (3-inch) gamma detectors around 1 kg cylindrical explosives (the radius of all cylindrical explosives samples is 5 cm) (the 2D view)

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In Fig. 8, the emitted neutron and photon beams from the e–γ–n converter are assumed in the direction of + Z-axis and the LaBr3 detectors were placed at a 90-degree angle relative to the + Z-axis, because in this direction there is a minimum of scattered photons. This is in agreement to the Klein–Nishina formula for Compton scattering [30]. In fact, in this study, we assumed that the neutron and photon beams emitted from the e–γ–n converter are cylindrical and parallel to the Z-axis. The assumption that the neutron beams are parallel can be acceptable and reasonable for two reasons, the first, increasing or decreasing the colliding neutrons with the explosive only leads to a change in the number of prompt gamma rays and no change in the overall shape of the prompt gamma spectrum (the reader can pay attention to the described equations in the next section). In fact, using the actual neutron angular distribution only reduces the number of prompt gamma rays (because the overall shape of the prompt gamma spectrum depends on the neutron energy spectrum or in the other words depends on the cross section of neutron capture reaction and it does not depend on the neutron flux) that can be solved by increasing the irradiation time and the second, using the assumption of parallel beams can very effectively help reduce the statistical error of the F8 tally and it enables us to do a good validation in the next section. In order to reduce statistical error, the diameter of the cylindrical beams of neutron and photon had been assumed 10 cm, because the diameter of 1 kg of the introduced cylindrical explosives is 10 cm and therefore all of the neutron and photon collide with cylindrical explosives. After doing the above, we perform Monte Carlo simulation for finding spectrum of prompt gamma rays of six explosives (TNT, PETN, RDX, HMX, NG, and EGDN) with mass 1 kg that in these spectrums the peaks of prompt gamma ray of H (2.223 MeV), N (10.829 MeV) and single escape (1.712 MeV & 10.318 MeV) clearly observed. For example, the spectrum of prompt gamma ray of TNT is shown in Fig. 9. Unfortunately, because of the low thermal neutron capture cross section of carbon and oxygen relative to hydrogen and nitrogen, their prompt gamma rays were not found in the gamma spectrum [43]. Note that the simultaneous observation of hydrogen and nitrogen prompt gamma peaks can be an indicator for detecting explosives.

Fig. 9
figure 9

The spectrum of prompt gamma (collected by twelve LaBr3 gamma detectors) of 1 kg cylindrical TNT by MCNPX

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It is good to mention that neutrons also activate lead as they pass through the shield (Fig. 4). Given that we assumed emitted photon beams from converter are parallel (described above) and also given the Compton angular distribution (described above), therefore, the probability of observation of prompt gamma of lead decreases in Fig. 9. If prompt gamma rays of lead are observed in the spectrum, but fortunately they cannot overlap with the peaks of H (2.223 MeV) and N (10.829 MeV), because the energy of the prompt gamma rays of lead are 6.737 MeV and 7.367 MeV [43]. Of course, in an experimental scenario, we may observe more prompt gamma peaks in Fig. 9 such as prompt gamma of aluminum, lanthanum and bromine. But according to Ref. [43] the prompt gamma ray energies of these materials are far from the peaks of H (2.223 MeV) and N (10.829 MeV). Even if the energy of their prompt gamma rays is a little close to the peaks of H and N but their neutron capture cross sections are much smaller [43]. Therefore, they cannot cause a significant problem in the peaks of H (2.223 MeV) and N (10.829 MeV). Of course, we can reduce the number of neutrons that may reach to detectors by adding collimator as well as appropriate shield. Another point that may lead to gamma spectrum disorder in experimental conditions, is the pile-up [30, 44]. The pile-up occurs when two or more gamma rays detected almost simultaneously in the detector. But this effect can be reduced significantly by specific electronic circuits and also algorithms [44, 45]. In the following, we studied and estimated some materials (including lead, cadmium, and boron) for the shielding of the LaBr3 detector. For this aim, we used a simple but practical geometry for the study of photon and neutron shielding as shown in Fig. 10.

Fig. 10
figure 10

The geometry used for the investigation of the shield (the radius of the cylindrical shield is related to the size of the detector window)

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For the investigation of the shielding of neutron and photon, a cylindrical shield (Fig. 10) has been exposed to radiation by the obtained neutron and photon beam from the converter (Fig. 1). Given that 83% of the neutrons emitted from the converter are thermal neutrons, the choice of boron and cadmium as a neutron shield can be good, because these two materials have a high thermal neutron absorption cross section [43]. On the other hand, boron has only one prompt gamma in 0.480 MeV energy and the maximum energy of prompt gamma of cadmium is 1.399 MeV that these energies are significantly different from the prompt gamma of hydrogen [43]. In Fig. 11, you can see the simulation results by F2 tally (flux averaged over a surface) of the MCNPX code for the three materials, lead (as the photon shield), cadmium, and boron. As shown in Fig. 11, boron has better results than cadmium, because boron, in addition to having a high absorption cross section for thermal neutrons, has a lower atomic number than cadmium, therefore it can also act as a moderator.

Fig. 11
figure 11

Particle flux after passing through the shield relative to the thickness of the shield

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4.2 Validation of TNAA

As mentioned above, the simultaneous presence of prompt gamma peaks of hydrogen and nitrogen can be used as a marker for detecting explosives, but it seems not enough for the accurate detection. Therefore, we must define another indicator which can be the ratio of the counts under the prompt gamma peaks of H (2.223 MeV) and N (10.829 MeV). We can calculate and compare the ratio for theory and the simulation. However, to calculate the ratio by simulation, we simply fit a Gaussian function onto the prompt gamma peaks of H and N (in Fig. 9). One can find good explanations on how to calculate counts under prompt gamma peaks based on gamma spectrum in Ref. [3]. To calculate the ratio by theory, we can begin from the following equation [3].

$$ R_{i} \left( {{\text{reactions}}/s} \right) = I\left( {\frac{\text{n}}{{{\text{m}}^{2} \;{\text{s}}}}} \right) \times N_{i} \left( {\frac{\text{nuclei}}{{{\text{m}}^{3} }}} \right) \times a\left( {{\text{m}}^{2} } \right) \times t\left( {\text{m}} \right) \times \sigma_{i} \left( {{\text{m}}^{2} } \right) $$
(2)

where \( R_{i} \) is the number of reactions per second for the ith prompt gamma, I is the neutron flux, N is the number of target ith nuclide per volume, a is the area of target, t is the thickness of the target and \( \sigma_{i} \) is the microscopic neutron cross section of ith prompt gamma. To reach the counts under prompt gamma peaks, it is enough that three parameters \( \in_{i} \), \( {{\varOmega }} \) and \( f_{i} \) multiply by \( R_{i} \). Therefore, we can write the counts under peak of ith prompt gamma (\( C_{i} \) in counts/s) as follows.

$$ C_{i} = I \times N_{i} \times a \times t \times \sigma_{i} \times \in_{i} \times {{\varOmega }} \times f_{i} $$
(3)

where \( \in_{i} \), \( {{\varOmega }} \) and \( f_{i} \) are the efficiency of ith prompt gamma peak (we can calculate it based on Fig. 8 by MCNPX, assuming the gamma rays are emitted exactly from the center of the circle with a 21 cm radius), the solid angle of detector (geometrical solid angle divided by 4π) and the factor of attenuation ith prompt gamma, respectively. Assuming all prompt gamma emit from the center of the cylindrical explosives, we can write the \( f_{i} \) as follows.

$$ f_{i} = \exp \left[ { - \left( {\frac{{\mu_{i} }}{\rho }} \right)\left( {\rho r} \right)} \right] $$
(4)

where \( \mu_{i} \) [46], ρ and r are total linear attenuation coefficient of ith prompt gamma in cm−1, the density of explosives in g/cm3 and the radius of cylindrical explosives in cm, respectively. Of course, we can write \( N_{i} \) as follows.

$$ N_{i} = \frac{{\rho N_{A} A_{i} }}{M} $$
(5)

where \( N_{A} \), \( A_{i} \) and \( M \) are Avogadro number, the number of ith element and the molecular weight (in g/mol) of explosives, respectively. Finally, as mention above, we can write the ratio of the counts under prompt gamma peaks of H and N as follows.

$$ \frac{{C_{{\left( {{\text{H}} - 2.223} \right)}} }}{{C_{{\left( {{\text{N}} - 10.829} \right)}} }} = \frac{{\sigma_{\text{H}} \in_{\text{H}} f_{\text{H}} A_{\text{H}} }}{{\sigma_{\text{N}} \in_{\text{N}} f_{\text{N}} A_{\text{N}} }} $$
(6)

The parameters of \( \sigma_{\text{H}} /\sigma_{\text{N}} \), \( \in_{\text{H}} / \in_{\text{N}} \), \( f_{\text{H}} /f_{\text{N}} \) and \( A_{\text{H}} /A_{\text{N}} \) are in Table 3 for the six explosives and also ratio of \( C_{\text{H}} /C_{\text{N}} \) both for theory and simulation and relative difference between them are shown in Table 3. See Table 3, the results of theory and simulation of ratio of the counts under prompt gamma peaks have a good agreement. There is a slight relative difference, which can be due to the assumptions we have made for theoretical calculations. According to Eq. 6, it is very good to mention that the overall shape of the prompt gamma energy spectrum is dependents on four parameters (\( \sigma \), \( \in \), \( f \) and \( A \)) and it does not depend on neutron flux. In fact, according to Eqs. 2 and 3, increasing or decreasing the neutron flux will only increase or decrease the number of prompt gamma rays.

Table 3 The ratio of \( C_{\text{H}} /C_{\text{N}} \) both for theory and simulation
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For the approximate detection time, we can mention Ref. [26]. In Ref. [26], the researchers used a Cf-252 with 5.4 × 107 (neutron/s) as neutron source along with ten BGO detectors for the detection of 1.2 kg HMX in one minute. Also, please pay attention to Ref. [47], the researchers report 9 and 12 MeV electron LINAC with average current of 800 and 1000 µA, respectively. Assuming an average current of 800 µA, the thermal neutron flux reach to 3.16 × 108 (n/cm2 s) in our work. Therefore, according to Refs. [26, 47], the explosives can be detected at a reasonable time.

5 Conclusion

In this paper, we investigated the feasibility of using a 10 MeV electron accelerator to detect explosives (TNT, PETN, RDX, HMX, NG, and EGDN) based on thermal neutron activation. To generate a suitable neutron source for detecting explosives, we designed and optimized an e–γ–n converter. Finally, we obtained 4.78 × 108 ± 0.63% (n/cm2 mA s) total neutron flux and 3.95 × 108 ± 0.69% (n/cm2 mA s) thermal neutron flux from the optimized e–γ–n converter. As seen above, a considerably good neutron source with a high and suitable thermal neutron flux was achieved. Twelve LaBr3 (3-inch) scintillator detectors were used for detection of explosives based on TNAA. The prompt gamma of H (2.233 MeV) and N (10.829 MeV) were observed in the gamma spectrum clearly which could be an indicator for detecting explosives. Another indicator is the ratio of the counts under the peaks corresponding to H and N which was verified with theory in this work. It should be noted that this conceptual design for explosives detection must be evaluated for radiation shielding, as done in Ref. [48]. Finally, it can be concluded that using a 10 MeV electron LINAC can be a good option for explosives detection and TNAA, if used with the appropriate gamma detectors.